Optical-Model Analysis of the Elastic Scattering of Alpha Particles

The elastic scattering of 22- and 40-Mev alpha particles on a variety of elements has been analyzed in terms of an optical model. The nuclear optical model potential assumed in this work has the form: $\frac{(V_R+i{V}_i)}{\{1+\exp [\frac{(r-r_1)}{d}\left]\right\}}$. The diffuse character of the electrical charge distribution in nuclei was also taken into account. The four parameters in the nuclear optical model potential were varied so as to obtain the best fit to the data. The diffuseness parameter is found to be $d\approx 0.5\times {10}^{-13\mathrm{}}$ cm and the parameter $r_1$, which represents an "average" radius of the nucleus-alpha particle system, is found to be $r_1\approx (1.35\mathrm{}{A}^{\frac{1}{3}}+1.3)\times {10}^{-13\mathrm{}}$ cm. The average values of $V_R$ and $V_i$ are -45 Mev and -10 Mev, respectively, at 40 Mev. Exceptions to this are the lightest elements, C, Al, and Ti, which require -30 Mev for $V_R$. At 22 Mev, $V_R$ is found to be -31 Mev. Other parameters have the same values obtained at 40 Mev.